Blender Texture/Model Seam Problems
Make sure to leave some space (a few pixels at least) between your UV pieces. Then turn on bleed in texture paint mode and when you bake things, so your texture extends beyond the boundaries of your model's UV coordinates. Doing both these things will avoid interpolation issues at the seams. There may be more issues in your case, but this is the first thing I would do to get rid of the seams.

*Bleed for texture painting is located in the Tool shelf > Options > Project Paint > Bleed. Increase the value to say 8.
For baking, the same thing is called Margin. But again, for either of these to be effective, you must first add some space between your UV pieces.